A fundamental investigation of gas/solid mass transfer in open-cell foams using a combined experimental and CFD approach

In this work, we combine numerical (CFD) simulations and experimental measurements in a fundamental investigation of the fluid-solid mass transfer properties of open-cell foams, which are promising support for catalytic applications limited by external heat and mass transfer. CFD simulations are exploited to gain insight into the complex transport mechanisms and to enable a parametric analysis of the geometrical features by means of virtually-generated structures. Catalytic activity experiments under diffusion control are used to validate the CFD results and to extend the range of conditions and foam morphologies investigated. Analysis of the flow field by CFD simulations provides a rational basis for the choice of the average strut size as a physically sound characteristic length for mass transfer correlations. Results from both numerical simulations and experimental tests are interpreted according to a fully-theoretically based geometrical model for the prediction of the specific surface area, which accounts for the detailed node-strut geometry. The effects of cell size and strut shape are properly included in the functional dependence of the Sherwood number on the Reynolds number. The effect of porosity requires one additional dependence, wherein the Sherwood number is inversely proportional to the square of the void fraction. The resulting Sherwood–Reynolds correlation is in excellent agreement with experimental data and CFD simulations. It enables accurate (±15%) estimation of the external mass transfer coefficients for open-cell foams when coupled with the proposed geometrical model from two readily accessible pieces of geometrical information, i.e. the void fraction and either the cell size or the pore diameter of the foam. The derived correlation can be applied to the design of novel enhanced open-cell foam catalyst substrates and structured reactors

A systematic procedure for the virtual reconstruction of open-cell foams

Open-cell foams are considered a potential candidate as an innovative catalyst support in many processes of the chemical industry. In this respect, a deeper understanding of the transport phenomena in such structures can promote their extensive application. In this contribution, we propose a general procedure to recover a representative open-cell structure starting from some easily obtained information. In particular, we adopt a realistic description of the foam geometry by considering clusters of solid material at nodes and different strut-cross sectional shapes depending on the void fraction. The methodology avoids time-consuming and expensive measuring techniques, such as micro-computed tomography (μCT) or magnetic resonance imaging (MRI). Computational Fluid Dynamics (CFD) could be a powerful instrument to enable accurate analyses of the complex flow field and of the gas-to-solid heat and mass transport. The reconstructed geometry can be easily exploited to generate a suitable computational domain allowing for the detailed investigation of the transport properties on a realistic foam structure by means of CFD simulations. Moreover, the proposed methodology easily allows for parametric sensitivity analysis of the foam performances, thus being an instrument for the advanced design of these structures. The geometrical properties of the reconstructed foams are in good agreement with experimental measurements. The flow field established in complex tridimensional geometries reproduces the real foam behavior as proved by the comparison between numerical simulations and experiments

A fundamental analysis of the influence of the geometrical properties on the effective thermal conductivity of open-cell foams

Structured catalysts have been proposed as a suitable solution for the efficient management of strongly exo- and endothermic processes. Among these structures, open-cell foams are considered as one of the most promising candidates as catalyst supports. In this work, we investigated the heat transfer in the solid matrix of open-cell foams by means of 3D numerical simulations carried out on virtually reconstructed structures. The totally interconnected solid matrix promotes high heat transfer rates because the conduction in the solid matrix is the main contribution to the heat transport. Our analysis reveals that the void fraction is the controlling parameter for the performances of the structures. An engineering correlation for the effective solid thermal conductivity has been derived, enabling a rational design of the foam geometry. Moreover, we analyzed the effect of the ratio between the node and strut diameters. We found that it has a strong influence on the heat conduction performance. High ratios penalize the heat transfer due to the reduced strut cross-section area at fixed porosity. On the other hand, an advanced design with a node-to-strut diameter ratio close to one can enhance the effective heat conductivity of open-cell foams up to 30%, improving the reactor performances compared to conventional open-cell foams

Coupling Euler–Euler and Microkinetic Modeling for the Simulation of Fluidized Bed Reactors: an Application to the Oxidative Coupling of Methane

We propose a numerical methodology to combine detailed microkinetic modeling and Eulerian–Eulerian methods for the simulation of industrial fluidized bed reactors. An operator splitting-based approach has been applied to solve the detailed kinetics coupled with the solution of multiphase gas–solid flows. Lab and industrial reactor configurations are simulated to assess the capability and the accuracy of the method by using the oxidative coupling of methane as a showcase. A good agreement with lab-scale experimental data (deviations below 10%) is obtained. Moreover, in this specific case, the proposed framework provides a 4-fold reduction of the computational cost required to reach the steady-state when compared to the approach of linearizing the chemical source term. As a whole, the work paves the way to the incorporation of detailed kinetics in the simulation of industrial fluidized reactors

A fast regression model for the interpretation of electrochemical impedance spectra of Intermediate Temperature Solid Oxide Fuel Cells

A frequency domain transformation method is applied to a physically consistent model of an IT-SOFC with MIEC electrolyte. Fast computation of the impedance spectra is achieved, which allows to apply the model to kinetic studies using traditional regressive techniques. The model includes conservation equations of mass and charge, gas diffusive transport effects and leakage current effects due to the semiconductor electrolyte. Global rate equations for the electrocatalytic semi-reactions guarantee economy of calibrated parameters. Two sets of impedance experiments collected on electrolyte-supported Cu-Pd-CZ80-SDC/SDC/LSCF-GDC cells are analyzed. The description of the H2 oxidation process is improved based on experiments with H2/N2 mixtures at fixed temperature and increasing H2 molar fraction (700 °C, 30–100% H2). The introduction of constant phase elements proves essential to closely predict Nyquist and Bode plots: strong inhomogeneity of the anode structure emerges, while the cathodic determining process is better identified via refinement of the double layer capacitance. Novel impedance experiments, performed with a CO-rich mixture (97% CO, 3% CO2) between 600 °C and 700 °C, allow to estimate the kinetic constant for CO electro-oxidation. The variation of the CPE parameters suggests that carbon deposition during exposure to CO simultaneously reduces the anodic active area and double layer capacitance

In situ adaptive tabulation for the CFD simulation of heterogeneous reactors based on operator-splitting algorithm

In situ Adaptive Tabulation algorithm is applied to efficiently solve the chemical substep in the context of the simulation of heterogeneous reactors. A numerical strategy—specifically conceived for unsteady simulation of catalytic devices—has been developed and interfaced, in the context of the operator splitting technique, with the solution of the chemical substep, which requires 70–90% of the total computational time. The algorithm performances have been illustrated by considering a single channel of a honeycomb reactor operating the catalytic partial oxidation of methane and a methane steam reforming packed bed reactor. The application of in situ adaptive tabulation resulted in a speed-up of the chemical substep up to ∼500 times with an overall speed-up of ∼5–15 times for the whole simulation. Such reduction of the computation effort is key to make affordable fundamental computational fluid dynamics simulations of chemical reactors at a level of complexity relevant to technological applications. © 2016 American Institute of Chemical Engineers AIChE J, 63: 95–104, 2017

Coupling CFD-DEM and microkinetic modeling of surface chemistry for the simulation of catalytic fluidized systems

In this work, we propose numerical methodologies to combine detailed microkinetic modeling and Eulerian-Lagrangian methods for the multiscale simulation of fluidized bed reactors. In particular, we couple the hydrodynamics description by computational fluid dynamics and the discrete element method (CFD-DEM) with the detailed surface chemistry by means of microkinetic modeling. The governing equations for the gas phase are solved through a segregated approach. The mass and energy balances for each catalytic particle, instead, are integrated adopting both the coupled and the operator-splitting approaches. To reduce the computational burden associated with the microkinetic description of the surface chemistry, in situ adaptive tabulation (ISAT) is employed together with operator-splitting. The catalytic partial oxidation of methane and steam reforming on Rh are presented as a showcase to assess the capability of the methods. An accurate description of the gas and site species is achieved along with up to 4 times speed-up of the simulation, thanks to the combined effect of operator-splitting and ISAT. The proposed approach represents an important step for the first-principles based multiscale analysis of fluidized reactive systems

Analytical Geometrical Model of Open Cell Foams with Detailed Description of Strut-Node Intersection

Open cell foams are regarded as potential enhanced catalyst carriers due to their high specific surface areas, low pressure drops, and good heat and mass transfer rates. However, it is difficult to evaluate their surface area. An analytical model is proposed, which is derived entirely from geometrical hypotheses and can be applied using different easily accessible input parameters. It can accurately estimate the specific surface and other features of foams for a wide range of porosities. The application of the new model to the reevaluation of published gas/solid mass transfer data is demonstrated

A quasi 2D model for the interpretation of impedance and polarization of a planar solid oxide fuel cell with interconnects

In this work, a one dimensional plus one dimensional (1D+1D) physical model of a high temperature solid oxide fuel cell (HT-SOFC) is presented. The model is distributed-charge and dynamic, and allows to predict polarization curves and impedance spectra of applicative sized planar cells (up to 10 cm x 10 cm) mounted between interconnects with rectangular ducts. The model solves rigorous conservation equations of mass, charge, momentum and energy, along the interconnect channels and within the cell's layers. The kinetic parameters of the hydrogen oxidation reaction and of the oxygen reduction reaction are fitted to a literature dataset measured between 700 °C and 800 °C, with a 20% H2, 5% H2O and 75% N2 mixture, on a standard anode-supported HT-SOFC (Ni-YSZ/YSZ/GDC/LSCF). Once calibrated, the model is used to study the evolution of local impedance spectra along the channel, as well as the occurrence of gradients of temperature, concentration, and current density within and along the cell structure. Remarkable differences emerge between global impedance spectra, based on the average current density extracted from the whole cell's surface, and local impedance spectra, based on the local current density value at each position along the channel. Local spectra reveal very specific features (negative-resistance arcs), which are absent in the average spectra, and which question the opportunity of collecting spatially resolved impedance measurements on a fine scale. The analysis of the steady state behavior highlights the severity of temperature gradients along the channel (150 K at 0.75 V and 50% H2 utilization factor), the onset of current density peaks, and the crucial role of interphase mass transport at the gas/electrode interface. The consequences of external diffusion on the polarization performance are analyzed, and the impact of different channel configurations on the local evolution of the spectra is explored